There has been interest in technologies for computer pattern recognition. For example, in Mathematical Neurobiology by J. S. Griffith (Academic Press, New York, 1971), models of neural networks are described. One model was a randomly connected network of neurons. Each neuron was either active (firing) or inactive. The total status of all the neurons defined the state of activity of the network. Since the neurons are connected to other neurons, any given state of activity would generate a next state of activity. Although the neuron connections were initially assigned at random, the connections remain fixed as the network moves from one state to the next. The total number of possible states is finite. Given any initial state, the network will step from state to state and ultimately hit a state that occurred previously. Since the network connections are fixed (deterministic), the network will continue to cycle through the same set of states. Given any arbitrary initial state the network always terminate in a cycle.
The above mentioned U.S. Pat. Nos. 4,504,970, 4,541,115, 4,550,431, 4,551,850, 5,473,707, and 5,473,708 describe various pattern recognition methods including using Associative Pattern Memory (APM) techniques to detect patterns.
Finite automata are a type of cellular automata that are the main focus of A New Kind of Science by Stephen Wolfram (Wolfram Media, Inc., 2002). In his book and other research papers, cycles are analyzed in depth.
There is a need for improved systems and methods for pattern recognition.